A membrane model for the response of thin plates to ballistic impact

The axisymmetric response of an infinite plate to an impacting projectile is determined analytically on the hypothesis that, for large deformations, a ductile plate behaves to a good approximation like a membrane under uniform tension. The lowest projectile velocity that results in perforation (the ballistic limit), and the residual velocity after perforation, then are determined on the basis of a critical-strain failure criterion. A figure of merit that depends only on the material properties of the target and characterizes the resistance of the material to impact appears naturally in the analysis. Variations in the ballistic limit with target thickness and projectile dimensions can be determined when this figure of merit is known. The theoretical ballistic limit and residual velocity for a steel cylinder impacting a titanium plate are found to agree with available measured values. Further support for the membrane model and an estimate of its range of validity are obtained by comparing the maximum displacement of an impulsively-loaded, circular membrane with experimental data for circular plates.     

Semi-theoretical analyses of the concrete plate perforated by a rigid projectile

Based on the three-stage perforation model, a semi-theoretical analysis is conducted for the ballistic performances of a rigid kinetic projectile impacting on concrete plates. By introducing the projectile resistance coefficients, dimensionless formulae are proposed for depth of penetration (DOP), perforation limit thickness, ballistic limit velocity, residual velocity and perforation ratio, with the projectile nosed geometries and projectile-target interfacial friction taken into account. Based on the proposed formula for DOP and lots of penetration tests data of normal and high strength concrete targets, a new expression is obtained for target strength parameter. By comparisons between the results of the proposed formulae and existing empirical formulae and large amount of projectile penetration or perforation tests data for monolithic and segmented concrete targets, the validations of the proposed formulae are verified. It is found that the projectile-target interfacial friction can be neglected in the predictions of characteristic ballistic parameters. The dimensionless DOP for low-to-mid speed impacts of non-flat nosed projectiles increases almost linearly with the impact factor by a coefficient of 2/(πS). The anti-perforation ability of the multilayered concrete plates is dependent on both the target plate thickness and the projectile impact velocity. The variation range of the perforation ratio is 1–3.5 for concrete targets.     

椭圆截面截卵形刚性弹体正贯穿加筋板能量耗散分析

为获得椭圆截面截卵形刚性弹体正贯穿加筋板的剩余速度,根据椭圆截面弹体贯穿靶板的破坏特征,认为贯穿过程中靶板的能量耗散方式主要为塞块剪切变形功与塞块动能、扩孔塑性变形功、花瓣动力功、花瓣弯曲变形功、靶板整体凹陷变形功、加强筋侧向凹陷变形功。推导了每种能量计算方法,计算中定量考虑了靶板扩孔、花瓣弯曲、凹陷变形的应变率效应。根据能量守恒关系,得到了椭圆截面弹体剩余速度和弹道极限速度预测公式。并通过实验结果对模型进行了验证。结果表明:考虑靶板应变硬化、应变率效应的贯穿模型可以准确预测弹体剩余速度;随着椭圆截面弹体长短轴之比的增大,靶板的弹道极限速度近似线性增大;长短轴之比小于3时,加筋板的主要耗能为花瓣弯曲变形能、整体凹陷变形能。     

钢球斜侵彻碳纤维复合材料板的实验研究

为了研究碳纤维复合材料板（CFRPs）在斜侵彻下的抗弹性能,利用一级轻气炮对碳纤维复合材料板进行了70~280 m/s速度范围的0°、30°和45°的侵彻贯穿实验,通过高速摄影技术测量了弹体速度和弹道轨迹。分析了冲击角度对弹道极限、能量吸收和弹道偏转的影响。结果表明:在冲击能量较低时,靶板在正冲击下的能量吸收率比斜冲击高,而当冲击能量较高时则恰好相反;此外,由于弹体穿过层合板的穿透长度随着冲击角度的增加而增加,弹道极限随着冲击角度的增加而增加;而冲击角度对弹道偏转的影响则随着冲击速度的变化而变化。     

Oblique Perforation of Thick Metallic Plates by Rigid Projectiles

Oblique perforation of thick metallic plates by rigid projectiles with various nose shapes is studied in this paper. Two perforation mechanisms, i.e., the hole enlargement for a sharp projectile nose and the plugging formation for a blunt projectile nose, are considered in the proposed analytical model. It is shown that the perforation of a thick plate is dominated by several non-dimensional numbers, i.e., the impact function, the geometry function of projectile, the non-dimensional thickness of target and the impact obliquity. Explicit formulae are obtained to predict the ballistic limit, residual velocity and directional change for the oblique perforation of thick metallic plates. The proposed model is able to predict the critical condition for the occurrence of ricochet. The proposed model is validated by comparing the predictions with other existing models and independent experimental data.The English text was polished by Keren Wang     

铝合金Whipple防护结构高速撞击实验研究

为了掌握航天器防护结构受空间碎片高速撞击的损伤破坏模式及其防护性能，采用二级轻气炮发射球形弹丸，对铝合金Whipple防护结构进行高速撞击实验研究。根据实验结果分析了铝合金Whipple防护结构的防护屏和舱壁在不同速度区间的损伤模式特征，以及薄铝板防护屏高速撞击穿孔和舱壁弹坑分布随弹丸直径、弹丸撞击速度变化的规律。通过固定弹丸直径，改变弹丸撞击速度，寻找临界撞击速度的方法获得了铝合金Whipple防护结构在0.5~5.5 km/s撞击速度区间内的撞击极限曲线，并与由Christiansen撞击极限方程得到的撞击极限曲线进行了比较，结果表明，实验最小临界弹丸直径略大于预测值。     

月牙形空腔结构金属靶的抗弹性能分析

为提高金属靶的抗弹性能,设计了一种含有月牙形空腔结构的金属靶。利用ABAQUS软件对月牙形空腔结构在12.7 mm穿甲燃烧弹弹芯侵彻下的弹体偏转性能进行了数值模拟研究,讨论了月牙形状、弹着点和空间排布对弹体偏转效果的影响。结果表明:月牙形状对弹体的偏转效果有显著的影响;空腔结构在不同弹着点表现出不同的弹体偏转性能,处于空腔胞元最薄弱处附近的弹着点弹体偏转角度明显小于其他位置;空腔胞元空间排布的非对称化处理能够提升空腔结构对子弹的偏转效果。     

Q235钢板对半球形头弹抗侵彻特性

利用轻气炮进行了半球形头杆弹正撞击单层板和等厚接触式三层板的实验, 得到了这两种结构靶体的初始-剩余速度曲线以及弹道极限。采用ABAQUS/EXPLICIT数值模拟软件对杆弹撞击金属板的过程进行了数值模拟研究, 通过对比数值模拟和实验结果, 验证了数值模拟材料模型和参数的有效性。研究了靶体结构对抗侵彻特性的影响, 并分析了弹体对靶体的撞击过程。研究结果表明:多层板的弹道极限高于等厚单层板。单层板主要失效模式为剪切, 而多层板的主要失效模式为整体的蝶形变形和局部的盘式隆起。对于多层板, 靶板具体的失效模式与其在靶中位置相关。     

Oblique impact by a spherical solid on a metal plate

The results of experimental studies of oblique impact by a spherical solid on a plane metal plate are presented. Plates made of AMTsM (plastic) and D16AT (rigid) alloys were used to determine the influence of the material characteristics on the impact aftereffects. The dependence of the ballistic limit on the angle of the impact velocity vector inclination to the plate plane was determined. The relationship between the ballistic limits of the oblique and normal impacts on the plate is established. The dependence of the ball motion trajectory refraction angles after collision with the plate on the ratio of the initial velocity to the ballistic impact is determined.     

碎片对铝合金薄板抗侵彻性能影响数值仿真研究

利用ABAQUS 有限元软件,采用合适材料参数及准则,建立平头弹及碎片撞击2A12-T4铝合金靶板的数值仿真模型。通过改变弹体与碎片之间的相对位置,研究弹体撞击靶板过程中碎片对其抗侵彻特性的影响规律及机理。通过数值仿真计算,分析弹体对靶体的撞击物理过程及失效机制。基于数值仿真计算结果可以发现,碎片对靶体抗侵彻性能受弹体速度以及弹体与碎片之间的相互位置等因素共同作用。对于靶体的抗撞击性能,弹体与碎片之间接触面积存在一个最佳值,接触面积太大或者太小都会减小靶板的损伤面积,从而减少撞击过程中靶板吸收的能量。     

细长尖头刚性弹对金属靶板的斜侵彻/穿甲分析

给出细长尖头刚性弹（如尖卵、尖锥形）斜侵彻/穿甲金属靶的一个分析模型。在细长尖头弹对中厚度金属靶的斜穿甲中,韧性孔洞扩张为主要的穿甲机理;着靶初期,发生方向角的改变。研究表明,金属靶的斜穿甲仅由4个量纲一参数控制,即冲击函数I、弹体几何函数N、量纲一靶厚和撞击斜角。分析得到显式的侵彻深度、终点弹道极限、剩余速度和撞击方向改变角表达式。该模型可预期跳飞发生的临界条件。理论预期与实验结果吻合较好。     

3D numerical simulations of ductile targets subjected to oblique impact by sharp nosed projectiles

Three-dimensional numerical simulations have been performed to study the behaviour of ductile targets subjected to normal and oblique impact by sharp nosed cylindrical projectiles. Twelve-mm-thick Weldox 460 E steel targets were impacted by 20 mm diameter projectiles with conical nose and 1-mm-thick 1100-H12 aluminum targets were impacted by 19 mm diameter ogive nosed projectiles. In both the cases, the targets were impacted at 0°, 15°, 30°, 45° and 60° obliquity or until the ricochet of the projectile occurred. The ballistic limit of 12 mm steel targets was found to be almost same up to 30° obliquity and thereafter it increased sharply. However, in the case of 1 mm aluminum targets a consistent increase in the ballistic limit was observed with increase in obliquity. The critical angle of projectile ricochet was found to increase with increase in impact velocity. Both the targets failed through ductile hole enlargement. Petal formation occurred in the aluminum targets and four petals were generally formed in each plate, however, the size of the upper two petals decreased and that of the lower two petals increased with increase in target obliquity. In the case of the steel targets the perforation occurred through the formation of a hole enclosed by a bulge. Both the bulge and the hole were circular in normal impact and elliptical in oblique impact. Petal formation in steel targets was observed at 60° obliquity. The ABAQUS/explicit finite element code was used to carry out numerical simulations.     

带前舱物的钝头弹对金属靶的正穿甲分析

进一步发展了考虑结构响应的剪切冲塞模型,计及前舱物的作用,对带前舱物的钝头弹穿甲金属靶的工程问题进行了刚塑性分析,用于分析终点弹道极限和剩余速度。除剪切破坏之外,模型还考虑了靶板弯曲、膜力拉伸和前舱物撞击引起的靶板预结构响应等。给出了简洁的终点弹道性能公式,与相关实验结果较吻合。     

Behaviour of uniaxially preloaded aluminium plates subjected to high-velocity impact

The purpose of this paper is to evaluate the behaviour of structural thin plates made of 7075-T6 aluminium alloy under normal impact of spherical steel projectiles, when they are subjected to uniaxial in-plane tensile preload. Also, nonloaded plates were tested under high-velocity impact. The impact and residual velocity were measured in all tests. From the relationships between the impact and residual velocities, the ballistic limit was estimated by a least-squares method. No significant differences were found between the ballistic limits under the two loaded conditions. Above the ballistic limit in the preloaded plates, unstable cracks that can generate the catastrophic failure of the plate were observed. At similar velocities, this phenomenon was not observed in nonloaded plates.     

串联随进战斗部垂直侵彻装甲钢板实验研究

设计了一种串联随进战斗部,作用时前级聚能装药形成聚能杆式侵彻体对靶板进行侵彻开孔,随后后级随进子弹依靠动能嵌入到开孔的靶板中,实现对目标的毁伤与封锁。在着靶速度为220～330m/s范围内,开展了对该串联战斗部垂直作用于不同厚度装甲钢板的侵彻实验研究。实验结果表明,在230～300m/s范围内,此种结构的串联随进战斗部可以有效作用,随进子弹的嵌入深度总体上随着撞击速度的提高而增大,随进子弹保持完整且嵌入牢固,能够有效实现对目标的毁伤与封锁。     

A3钢钝头弹撞击45钢板破坏模式的试验研究

为了研究破片模拟弹的终点弹道效应,进行了不同质量A3钢钝头弹(弹径25 mm)撞击45钢板的试验研究,其中A3钢强度弱于45钢。在约200～800 m/s的撞击速度范围内,随着撞击速度的增加,分别观察到弹体出现泰勒撞击、向日葵型花瓣帽形失效及靶板冲塞穿甲三种破坏模式。伴随弹体和靶体经历的不同结构破坏模式,弹材和靶材也经历着相当复杂的材料失效。     

Elastic–plastic contact force history and response characteristics of circular plate subjected to impact by a projectile

A new elastic–plastic impact–contact model is proposed in this paper. By adopting the principle of minimum acceleration for elastic–plastic continue at finite deformation, and with the aid of finite difference method, the proposed model is applied in the problem of dynamic response of a clamped thin circular plate subjected to a projectile impact centrally. The impact force history and response characteristics of the target plate is studied in detail. The theoretical predictions of the impact force and plate deflection are in good agreements with those of LDA experimental data. Linear expressions of the maximum impact force/transverse deflection versus impact velocity are given on the basis of the theoretical results. The project supported by the National Natural Science Foundation of China (10532020).     

弹体高速侵彻钢筋混凝土靶试验研究

为研究结构弹体对钢筋混凝土靶的高速侵彻破坏效应,利用口径35 mm弹道炮开展了1 030～1 520 m/s速度范围内的高速侵彻试验,获得了弹体的撞击速度、破坏形态、剩余长度、剩余质量和靶体中的侵彻深度及成坑尺寸等试验数据,分析了侵彻深度和侵彻机理随速度的变化关系。结果表明:在1 030～1 390 m/s的速度范围内,弹体头部磨蚀,磨蚀程度随侵彻速度增加而加剧,侵彻深度随撞击速度近似线性增大;撞击速度在1 390～1 480 m/s范围内,弹体头部严重磨蚀,侵彻深度随撞击速度增加而减小;撞击速度大于1 480 m/s后,弹体严重破碎,侵彻深度急剧下降。针对结构弹体高速侵彻过程中的破坏特点,将侵彻速度划分为刚体侵彻区、准刚体侵彻区、侵蚀体侵彻区和破碎体侵彻区,可为钻地弹结构设计提供参考。     

An investigation of oblique perforation of metallic plates by projectiles

An experimental and analytical study was performed on the mechanics of oblique perforation of metallic plates by projectiles. The purpose was to determine the dependence of the velocity drop on the angle of impact for prescribed mechanical and physical properties of the projectile and the target plate. The ballistic experiments were carried out with 0.22-in.-caliber lead bullets on target plates of commercially pure aluminum and an aluminum alloy which ranged from 2.0 to 6.0 mm in thickness. Transient measurements were taken which included high-speed photographs of the perforation process. The theoretical model that had been developed previously by the authors for the case of normal perforation was modified to include the effects of the angle of impact. The experimental observations for the present test conditions indicate that the main modification to the analysis is the use of the total projectile path as the effective target-plate thickness. Reasonably good agreement between the experimental and theoretical results was obtained.     

依兰陨石坑形成过程数值模拟研究

基于iSALE-2D仿真代码对依兰陨石坑的形成过程进行了研究,采用欧拉算法开展数值模拟,探讨了依兰陨石坑的撞击条件,统计分析了成坑过程中熔化层的形成与分布规律,结合点源成坑相似律模型,拟合得到强度机制下的成坑半径关系式。研究结果表明一颗直径120 m、撞击速度12 km/s的花岗岩质小行星垂直撞击地表形成一个与依兰陨石坑形态相似的陨石坑,再现了成坑形成的3个阶段：接触与压缩阶段、开坑阶段、后期调整阶段。大部分熔体在坑底呈分层堆叠分布,少量熔体随抛射物沉积在靶体表面,呈离散状分布,完全熔化材料质量约为撞击体质量的24倍。直径120 m、撞击速度12 km/s工况模拟结果与拟合的成坑半径关系式结果相对误差10.3%。